The phrase “to chew the rag” means to talk, or to make a speech; especially, to talk at length, to grumble continuously, or to rant.
As with any slang expression, the parentage and time of birth of this cannot be positively determined.
Records of written use are simultaneous in England and the United States, in 1885, army slang in England, newspaper use in this country; so it is certain that the man in the street of either country had been using the expression a long time before that. But this noun, rag, we think, never had any connection with the ordinary rag, a strip of cloth.
It seems to have been formed from the verb, to rag, which, in dialectal English back in the eighteenth century, meant, to scold; hence, to annoy, tease; also, to wrangle. No one knows the source of this “rag,” but it is supposed to have been a contraction of “bully-rag.”
As to chewing, in this figurative sense pertaining to words, we can find that use in Shakespeare. In Measure for Measure, he has Angelo chewing a name; that is, saying it over and over.
And away back in the sixteenth century, the expression, “to chew the cud,” meaning to ruminate upon a matter, was already proverbial.